Comparison of three‐dimensional analysis and stereological techniques for quantifying lithium‐ion battery electrode microstructures

Lithium‐ion battery performance is intrinsically linked to electrode microstructure. Quantitative measurement of key structural parameters of lithium‐ion battery electrode microstructures will enable optimization as well as motivate systematic numerical studies for the improvement of battery performance. With the rapid development of 3‐D imaging techniques, quantitative assessment of 3‐D microstructures from 2‐D image sections by stereological methods appears outmoded; however, in spite of the proliferation of tomographic imaging techniques, it remains significantly easier to obtain two‐dimensional (2‐D) data sets. In this study, stereological prediction and three‐dimensional (3‐D) analysis techniques for quantitative assessment of key geometric parameters for characterizing battery electrode microstructures are examined and compared. Lithium‐ion battery electrodes were imaged using synchrotron‐based X‐ray tomographic microscopy. For each electrode sample investigated, stereological analysis was performed on reconstructed 2‐D image sections generated from tomographic imaging, whereas direct 3‐D analysis was performed on reconstructed image volumes. The analysis showed that geometric parameter estimation using 2‐D image sections is bound to be associated with ambiguity and that volume‐based 3‐D characterization of nonconvex, irregular and interconnected particles can be used to more accurately quantify spatially‐dependent parameters, such as tortuosity and pore‐phase connectivity.     

颗粒群特征的定量体视学分析方法

根据定量体视学原理，应用Ｑｕａｎｔｉｍｅｔ６００图象分析仪，对颗粒群特征参数进行了定量分析，并对定量体视学方法实验参数：最小样本数、图像优化方法及二值化灰度阀值等进行了实验研究．实验结果表明：定量体视学图像分析方法可同时获得矿渣微粉试样的级配和颗粒形状因子（圆度）等一系列颗粒群特征参数     

A new stereological principle for test lines in three-dimensional space

A new principle is presented to generate isotropic uniform random (IUR) test lines hitting a geometric structure in three-dimensional space (3D). The principle therefore concerns the estimation of surface area, volume, membrane thickness, etc., of arbitrary structures with piecewise smooth boundary. The principle states that a point-sampled test line on an isotropic plane through a fixed point in 3D is effectively an invariant test line in 3D. Particular attention is devoted to the stereology of particles, where an alternative to the surfactor method is obtained to estimate surface area. An interesting case arises when the particle is convex. The methods are illustrated with synthetic examples.     

Quantifying Thermal Spray Coating Architecture by Stereological Protocols: Part I. A Historical Perspective

This article presents, from a historical perspective, some stereological protocols of the first order. Such protocols can be implemented to quantify statistically the architecture of thermal spray coatings and their relevant features (pores, lamellas, etc.). A forthcoming Part II of this article will address some key points to implement, from a practical point of view, such protocols.

体视学及其在古陶瓷中的应用

本文以古陶瓷复相显微结构图像为研究对象,利用体视学方法分析古陶瓷中釉的各相参数,并对其进行定量表征,为古陶瓷的研究与应用提供数据依据.     

掺钕钇铝石榴石透明陶瓷 (Nd:YAG)体视学研究

采用低温燃烧法合成出掺钕钇铝石榴石(Nd：YAG)粉末,经模压300MPa成型,于1700℃真空烧结5h,制备出尺寸φ9mm×1mmNd：YAG透明陶瓷片．对Nd：YAG透明陶瓷片进行光透过率、场发射-环境扫描电镜测量．采用体视学原理与方法定量地研究了Nd：YAG透明陶瓷的微观结构参数和光透过率之间的关系．研究结果表明：尺寸φ9mm×1mmNd：YAG透明陶瓷片在可见光波段光透过率约为45％,在近红外光波段约为55％；随着入射光波长的增加,光透过率增加；随着晶粒三维球当径(D_(3S))的增加,光透过率增加,当D_(3S)约为20μm时,Nd：YAG透明陶瓷光透过率接近单晶理论值；随着晶粒以及单个晶粒平均比表面积的增加,光透过率降低；随着晶粒三维平均自由距离的增加,光透过率降低．     

Semi-automated measurement of true chord length distributions and moments by video microscopy and image analysis

The distribution of the lengths of airspace chords in pulmonary parenchyma characterizes many architectural features of the alveoli and alveolar ducts. Laborious to obtain manually, the distributions and density functions may be acquired semi-automatically by video microscopy, digitization and image processing. The accuracy of the estimation is influenced by the microscopical methods and also by the techniques used (i) to convert the digitized grey-scale picture to a two-valued image, (ii) to collect the chord lengths and (iii) to compensate for finite field widths. The last problem arises because some chords are completely visible within a field while others are only partially seen, since one of the two air-tissue boundaries lies outside the field of view. This error systematically biases the observed distribution. This paper contains solutions to hardware, software and analytic problems encountered while developing the capability to measure airspace chord length density functions semi-automatically. Formulas for estimating the true chord length density function from samples of observed chord lengths are presented. Also given are formulas for the estimation of the first and second moments of the true chord length distribution from the means of observed chord lengths. These techniques of image preparation and analysis should be suitable for characterizing particle, grain or cell size distributions, especially where many profiles fall partially outside the field of view.     

Estimation of length and surface of anisotropic capillaries

Surface density (S_V) and length density (L_V) of myocardial capillaries have hitherto been estimated from their profile boundary length (B_A) and their numerical density (Q_A) on transverse sections by the simplifying assumptions of the Krogh model (perfectly anisotropic, straight, unbranched capillaries with constant cross-sectional area). As the capillaries actually are partially anisotropic, curved, branching cylinders with variable cross-sectional area, a geometrical bias arises from the model-reality discrepancies. We have applied and compared two methods to overcome these inconsistencies: (1) estimation of L_V and S_V by a more realistic model (the Dimroth-Watson distribution); (2) estimation of L_V and S_V from isotropic uniform random (IUR) sections. Twelve male Wistar rats were fixed by retrograde vascular perfusion. One pair of longitudinal and transverse sections, and six IUR sections per animal were selected at random from the left ventricular papillary muscles. Ultrathin sections were silver-impregnated and studied by light microscopic morphometry. Nearly identical estimates of L_V and S_V were found by both methods. The model-based estimation provides biologically meaningful anisotropy constants, but it presupposes knowledge of the anisotropy axis. The IUR method provides no measure of anisotropy, but it can be applied in tissues where the anisotropy axis is not known. Both methods are equally efficient and practically unbiased in S_V estimation, but the model-based estimation is far more efficient in L_V estimation.     

计算混凝土中邻近集料表面间距平均值的体视学方法

借助于体视学中的平均自由程公式,给出了计算水泥基复合材料平均邻近集料表面间距平均值的方法,并给出了两种计算集料的表面积的方法：基于集料表面积近似计算的解析解法和混凝土样品截面的线采样分析法．结果表明：采用截面线采样分析法能够很好地近似计算混凝土中邻近集料表面间距的平均值,也提供了一种计算不规则形状集料粒子体系表面积的思路,混凝土中邻近集料表面间距的平均值大小只与混凝土中集料的体积分数、集料的密度以及集料的比表面积有关,而与集料的粒径分布（或粒径范围）无关．